Engineering Mechanics

Contents

1. Fundamentals of Mechanics  

• 1.1 Introduction   
• 1.2 Basic Dimensions and Units  of Mechanics,   
• 1.3 Secondary Dimensional Quantities
• 1.4 Law of Dimensional Homogeneity
• 1.5 Dimensional Relation between  Force and Mass   
• 1.6 Units of Mass   
• 1.7 Idealizations of Mechanics   
• 1.8 Vector and Scalar Quantities   
• 1.9 Equality and Equivalence  of Vectors   
• 1.10 Laws of Mechanics

2. Elements of vector Algebra

• 2.1  Introduction   
• 2.2 Magnitude and Multiplication of a Vector by a Scalar
• 2.3 Addition and Subtraction of Vectors
• 2.4 Resolution of Vectors; Scalar Components
• 2.5 Unit Vectors 
• 2.6 Useful Ways of Representing Vectors
• 2.7 Scalar or Dot Product of Two Vectors
• 2.8 Cross Product of Two Vectors
• 2.9 Scalar Triple Product
• 2.10 A Note on Vector Notation

3. Important vector Quantities

• 3.1 Position Vector
• 3.2 Moment of a Force about a Point
• 3.3 Moment of a Force about an Axis
• 3.4 The Couple and Couple Moment
• 3.5 The Couple Moment as a Free Vector
• 3.6 Addition and Subtraction of Couples
• 3.7 Moment of a Couple About a Line 
   

4. Equivalent Force Systems

• 4.1 Introduction
• 4.2 Translation of a Force to a Parallel Position
• 4.3 Resultant of a Force System
• 4.4 Simplest Resultants of Special Force Systems
• 4.5 Distributed Force Systems
   

5. Equations of Equilibrium

• 5.1 Introduction 
• 5.2 The Free-body Diagram
• 5.3 Free Bodies Involving Interior Sections
• 5.4 Looking Ahead?Control Volumes
• 5.5 General Equations of Equilibrium
• 5.6 Problems of Equilibrium I 
• 5.7 Problems of Equilibrium II 
• 5.8 Two Point Equivalent Loading
• 5.9 Problems Arising from Structures
• 5.10 Static Indeterminacy
   

6.   Introduction to structural Mechanics

Part A: Trusses

• 6.1 The Structural Model
• 6.2 The Simple Truss
• 6.3 Solution of Simple Trusses
• 6.4 Method of Joints
• 6.5 Method of Sections
• 6.6 Looking Ahead?Deflection of a Simple, Linearly Elastic Truss

Part B: Section Forces in Beams

• 6.7 Introduction
• 6.8 Shear Force, Axial Force, and Bending Moment
• 6.9 Differential Relations for Equilibrium

Part C: Chains and Cables

• 6.10 Introduction
• 6.11 Coplanar Cables; Loading is a Function of x
• 6.12 Coplanar Cables: Loading is the Weight of the Cable Itself

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7. Friction Forces

• 7.1 Introduction
• 7.2 Laws of Coulomb Friction
• 7.3 A Comment Concerning the Use of Coulomb's Law
• 7.4 Simple Contact Friction Problems
• 7.5 Complex Surface Contact Friction Problems
• 7.6 Belt Friction
• 7.7 The Square Screw Thread
• 7.8 Rolling Resistance
   

8.   Properties of Surfaces

• 8.1 Introduction
• 8.2 First Moment of an Area and theCentroid
• 8.3 Other Centers
• 8.4 Theorems of Pappus-Guldinus
• 8.5 Second Moments and the Product of Area of a Plane Area
• 8.6 Tranfer Theorems
• 8.7 Computations Involving Second Moments and Products of Area
• 8.8 Relation Between Second Moments and Products of Area
• 8.9 Polar Moment of Area
• 8.10 Principal Axes
   

9.    Moments and Products of Inertia

• 9.1 Introduction
• 9.2 Formal Definition of Inertia Quantities
• 9.3 Relation Between Mass-Inertia Terms and Area-Inertia Terms
• 9.4 Translation of Coordinate Axes
• 9.5 Transformation Properties of the Inertia Terms
• 9.6 Looking Ahead?Tensors
• 9.7 The Inertia Ellipsoid and Principal Moments of Inertia

10.   Methods of Virtual Work and Stationary Potential Energy

• 10.1    Introduction

Part A: Method of Virtual Work

• 10.2 Principle of Virtual Work for a Particle
• 10.3 Principle of Virtual Work for Rigid Bodies
• 10.4 Degrees of Freedom and the Solution of Problems
• 10.5    Looking Ahead?Deformable Solids

Part B: Method of Total Potential Energy

• 10.6 Conservative Systems
• 10.7 Condition of Equilibrium for a Conservative System
• 10.8 Stability
• 10.9 Looking Ahead?More on Total Potential Energy

11. Kinematics of a Particle?Simple Relative Motion

• 11.1    Introduction

Part A: General Notions

• 11.2    Differentiation of a Vector with Respect to Time

Part B: Velocity and Acceleration Calculations

• 11.3 Introductory Remark
• 11.4 Rectangular Components
• 11.5 Velocity and Acceleration in Terms of Path Variables
• 11.6 Cylindrical Coordinates

Part C: Simple Kinematical Relations and Applications

• 11.7 Simple Relative Motion
• 11.8 Motion of a Particle Relative to a Pair of Translating Axes
   

12. Particle Dynamics

• 12.1    Introduction

Part A: Rectangular Coordinates; Rectilinear Translation

• 12.2 Newton's Law for Rectangular Coordinates
• 12.3 Rectilinear Translation
• 12.4 A Comment

Part B: Cylindrical Coordinates; Central Force Motion

• 12.5 Newton's Law for Cylindrical Coordinates
• 12.6 Central Force Motion? An Introduction
• 12.7 Gravitational Central Force Motion
• 12.8 Applications to Space Mechanics

Part C: Path Variables

• 12.9    Newton's Law for Path Variables

Part D: A System of Particles

• 12.10 The General Motion of a System of Particles

13.    Energy Methods for Particles

Part A: Analysis for a Single Particle

• 13.1 Introduction
• 13.2 Power Considerations
• 13.3 Conservative Force Field
• 13.4 Conservation of Mechanical Energy
• 13.5 Alternative Form of Work-Energy Equation

Part B: Systems of Particles

• 13.6 Work-Energy Equations
• 13.7 Kinetic Energy Expression Based on Center of Mass
• 13.8 Work-Kinetic Energy Expressions Based on Center of Mass
   

14. Methods of Momentum for Particles

Part A: Linear Momentum

• 14.1 Impulse and Momentum Relations for a Particle
• 14.2 Linear-Momentum Considerations for a System of Particles
• 14.3 Impulsive Forces
• 14.4 Impact
• 14.5 Collision of a Particle with a Massive Rigid Body

Part B: Moment of Momentum

• 14.6 Moment-of-Momentum Equation for a Single Particle
• 14.7 More on Space Mechanics
• 14.8 Moment-of-Momentum Equation for a System of Particles
• 14.9 Looking Ahead?Basic Laws of Continua

 
15. Kinematics of Rigid Bodies; Relative Motion

• 15.1 Introduction
• 15.2 Translation and Rotation of Rigid Bodies
• 15.3 Chasles'Theorem
• 15.4 Derivative of a Vector Fixed in a Moving Reference
• 15.5 Applications of the Fixed-Vector Concept
• 15.6 General Relationship Between Time Derivatives of a Vector for Different References
• 15.7 The Relationship Between Velocities of a Particle for Different References
• 15.8 Acceleration of a Particle for Different References
• 15.9 A New Look at Newton's Law
• 15.10 The Coriolis Force

 16. Kinetics of Plane Motion of Rigid Bodies

• 16.1 Introduction
• 16.2 Moment-of-Momentum Equations
• 16.3 Pure Rotation of a Body of Revolution About its Axis of Revolution
• 16.4 Pure Rotation of a Body with Two Orthogonal Planes of Symmetry
• 16.5 Pure Rotation of Slablike Bodies
• 16.6 Rolling Slablike Bodies
• 16.7 General Plane Motion of a Slablike Body
• 16.8 Pure Rotation of an Arbitrary Rigid Body
• 16.9 Balancing

17. Energy and Impulse-Momentum Methods for Rigid Bodies 

• 17.1      Introduction

Part A: Energy Methods 

• 17.2 Kinetic Energy of a Rigid Body  
• 17.3 Work-Energy Relations  

Part B: Impulse-Momentum Methods 

• 17.4 Angular Momentum of a Rigid Body About Any Point in the Body
• 17.5 Impulse-Momentum Equations
• 17.6 Impulsive Forces and Torques: Eccentric Impact 
   

18. Dynamics of General Rigid-Body Motion

• 18.1 Introduction
• 18.2 Euler's Equations of Motion
• 18.3 Application of Euler's Equations
• 18.4 Necessary and Sufficient Conditions for Equilibrium of a Rigid Body
• 18.5 Three-Dimensional Motion About a Fixed Point; Euler Angles
• 18.6 Equations of Motion Using Euler Angles
• 18.7 Torque-Free Motion
   

19. Vibrations

• 19.1 Introduction
• 19.2 Free Vibration 
• 19.3 Torsional Vibration 
• 19.4 Examples of Other Free-Oscillating Motions 
• 19.5 Energy Methods 
• 19.6 Linear Restoring Force and a Force Varying Sinusoidally with Time 
• 19.7 Linear Restoring Force with Viscous Damping
• 19.8 Linear Restoring Force, Viscous Damping, and a Harmonic Disturbance 
• 19.9 Oscillatory Systems with Multi-Degrees of Freedom